Solving the Korteweg-de Vries equation with Hermite-based finite differences

The Korteweg-de Vries (KdV) equation is extensively studied in the field of nonlinear waves, with one key tool for this being fast and accurate numerical algorithms. Finite difference (FD) and pseudo-spectral (PS) methods are commonly used. We discuss here the pros and cons in this application area for a new class of Hermite-based finite difference (HFD) methods. Their most notable characteristic is to remain more ‘local’ than FD approximations for increasing orders of accuracy, translating into smaller error constants.